pub fn new_birthday_probability(n: u32) -> f64 {
    if n <= 2 {
        panic!("Invalid input");
    }
    let mut p = 1.0;
    for i in 1..=n {
        p *= (365 - i + 1) as f64 / 365.0;
    }
    return 1.0 - p;
}
